Ms Le Pen told France2: “I want to offer France a referendum on the death penalty. Personally, I feel that this possibility should exist.
“I always said that I would offer French citizens the possibility to express themselves on the topic through a referendum.”
The death penalty was abolished in France in 1981.
The controversial leader claimed radical Islam was behind the attacks and said “denial and hypocrisy” are no longer an option, according to ITV.
“The absolute refusal of Islamic fundamentalism must be proclaimed high and loud by whomever. Life and liberty are among the most precious values.”
Ms Le-Pen’s Front National party harnessed anti-immigration and anti-EU sentiment in France to win control of 11 towns and more than 1,400 municipal seats nationwide in the local elections in April.
Tensions are now growing in France as police continue to hunt for two men in connection with the brutal attack. Twelve people were killed by gunmen who stormed the Paris headquarters of the satirical magazine.
Some fear Wednesday's attack could be used to feed anti-Islamic agitation after it was reported the gunmen shouted "Allahu akbar" before embarking on the massacre.
On Thursday, a makeshift explosive device was detonated outside a kebab restaurant close to a mosque in eastern France, although police have not drawn a direct link with the Charlie Hebdo attack.
Two shots were fired at a Muslim prayer hall at Port la Nouvells in Aude in southern France.
After a series of Islamaphobic posts on Twitter, #BlameTheMuslimGame began trending mocking the users responsible for those tweets.